Stat 210B Homework Assignment 5
(due April 3)
1. Suppose
bardbl
P
n

Q
n
bardbl →
0. Show that
P
n
and
Q
n
are mutually contiguous.
2. Suppose, under
P
n
,
X
n
=
Y
n
+
o
P
n
(1). Suppose
Q
n
is contiguous to
P
n
. Show that
X
n
=
Y
n
+
o
Q
n
(1).
3. Suppose
P
θ
is the uniform distribution on (0
, θ
).
Let
P
n
θ
denote the distribution of
n
iid
draws from
P
θ
. Fix
h
and determine whether or not
P
n
1
and
P
n
1+
h/n
are mutually contiguous.
Consider both
h >
0 and
h <
0.
4. Let
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 Fall '05
 MICHAELJORDAN
 Normal Distribution, Probability, Probability theory, probability density function, Equals sign, Qn, Stat 210B Homework

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